Ex Libris C. K. OGDEN THE P U T- A N D-C A L L ABERDEEN UNIVERSITY PRESS. THE PUT-AND-CALL BY LEONARD R. HIGGINS LONDON EFFINGHAM WILSON ROYAL EXCHANGE 1896 All rights reserved TO MY ESTEEMED FRIEND, MR. E. HEDLEY CUTHBERTSON ; THIS LITTLE VOLUME IS Respectfully 2>eMcateJ>. 20153C7 PREFACE. THE writer of the following pages feels that, in publishing this little book on Options, he may be telling many of his professional friends what they already know perhaps better than the author. If, however, he succeeds in supplying in a read- able form an answer to the question which has so often been put to him by the uninitiated, viz. t " What is an Option ? " and in placing before those who have mastered the intricacies of Option deal- ing the Theory of the "Value of the Put-and- Call " in a somewhat new light, the object of his little book will be attained. June, 1896. TABLE OF CONTENTS. PREFACE. CHAPTER I. INTRODUCTION. PAGES The Legality of Option Dealing Day to Day Options The Stock Exchange Settlement Contango and Backwardation-Ecart " Distance " 1-5 CHAPTER II. DEFINITION. Option Call Put Put-and-Call Call o' More Put o' More Option Money The Giver The Taker 6-9 CHAPTER III. WORKING THE SINGLE OPTION. A Favourable Call of Brighton "A" An Unsuccessful Call of the Same Stock A Successful Put of Spanish 4/ A Call of Rio Tinto Shares A Put of Rio Tinto Shares The Conversion of One Option into Another 10-17 CHAPTER IV. WORKING THE DOUBLE OPTION. The Advantage of the Double Option A Put-and-Call of Louisville and Nashville Shares The Put-and-Call turned into a Call A Put-and-Call of Milwaukee Shares A Put-and-Call of Erie Shares alike Profitable to the Giver and the Taker of the Option Money 18-25 CHAPTER V. THE CONVERSION OF OPTIONS. Rules How the Option Money is Affected and the Option Price remains the Same 26-30. CHAPTER VI. THE PRINCIPLES FORMULATED. More Conversions of Options Selling Against a Call Over the Option Price Selling Against a Call Under the Option Price How the " Money " is Affected Formulae Examples Fixing the Option Price Above or Below the "Right Place" The "Distance" - 31-39 viii CONTENTS. CHAPTER VII. THE CALL o' MORE PUT o' MORE. PAGES Conversion of Call o' More into Call or Put-and-Call Four Different Ways of Doing One Transaction Formulas for Call o' More and Put o' More ----. 40-48 CHAPTER VIII. THE CALL OF TWICE MORE, THREE TIMES MORE, ETC. The " Distance " Determined Formulae Why not Exactly Appli- cable in Practice Exercise 49-53 CHAPTER IX. THE SINGLE OPTION DISGUISED. Difficulty of Dealing in Firm Stock for the Option Period Discussed The Put-and-Call Sometimes Relatively Cheaper than the Single Option Giving for the Put-and-Call Instead of the Single Option to Disguise One's Position Illustration 54-57 CHAPTER X. OPTION-DEALING ABROAD. London the Option Market of the World Paris Berlin English Superior to French and German in Expressing Optional Transac- tions English, French, and German Vocabulary - - - - 58-63 CHAPTER XL THE VALUE OF THE PUT-AND-CALL. Options Compared to Insurance Estimating the Risk Average Fluctuation the Basis of Estimate Points of Difference between Option Dealing and Orthodox Insurance Must be Sufficient Busi- ness to Establish an Average The Giver of Option Money and the Insurer Contrasted Essential Conditions in Taking Option Money Market Quotations for Options Compared with Average Fluctuations Table of Average Values 64-76 CHAPTER I. INTRODUCTION. THE Committee of the London Stock Exchange re- cognise the legality of optional dealings in stocks and shares provided that the option period does not exceed two accounts beyond that for which bargains are being currently made ; but they will not legislate upon any dis- pute arising from an option transaction done for a longer period, nor can a claim be made against a defaulter's estate in respect of any such unrecognised bargain. Rule 90, applicable to registered stocks, says: "The committee will not recognise any bargain in shares or stocks effected for a period beyond the ensuing two accounts " ; and Rule 1 1 2 relating to securities to bearer is to the same effect.* In spite of these disadvantages, however, options for two or three months, and even further ahead, are * It must be stated, however, that the above-mentioned rules do not apply to English, India, Corporation and Colonial Govern- ment Inscribed Stocks, for under this heading Rule 79 reads : "The committee will not recognise any bargain for a future account if it shall have been effected more than eight days pre- vious to the close of the pending account". INTRODUCTION. easily negotiated in the London market ; in fact, the " option period " may be said to range from a few hours to six months. Day-to-day options are not so largely dealt in as they were in former years, many of the persistent takers of " day-to-day money " having found that the risks involved were not sufficiently covered by the small amount of "money" given, and that the practice had a tendency to encourage the running of a large, unprofitable " book". The " call o' more to-morrow " and " put o' more to-morrow " still survive ; for, on the one hand, such transactions are frequently found by parties interested in engineering a rise or a fall to be useful in puffing or depressing the stock which is the object of their attention, and, on the other hand, provide a more profitable method of taking option money, as the real amount of premium involved in a " call o' more " transaction is greater than would appear at first sight from the difference between the market price and the option price of the stock. " Puts" and " calls" of stocks are commonly done for one week and for one account, but the majority of the options negotiated in the London market are for one month, two months, and three months on. It may be of interest to mention that dealings in the London Stock Exchange are settled twice every month, the dates of the settlements (which are fixed by the committee three accounts in advance) falling about the middle and end of each month. The length of the account ranges from thirteen to nineteen days INTRODUCTION. 3 and the settlement occupies three days, called respec- tively, "contango day," "ticket day," and "settling" or " account day ". On the contango day all stocks not being paid for or delivered are "carried over" to the following account at a " making-up " price, which is fixed by the official broker or by the market, those persons who are unable or unwilling to pay for stock bought giving a market rate of interest to those who have money to lend. It sometimes happens that dealers or speculators, who have sold more stock than they can conveniently deliver, have to pay a fine for non-delivery to those who have bought it. The postponement of delivery is arranged on the contango day, and the fine imposed is called a " backwardation " or " back ". On the second day of the settlement or " Ticket day " the names and addresses of the persons for whom brokers have bought registered stock are given to the sellers on what is called a ticket. This ticket also bears the name of the member paying for the stock and the price at which the transaction is done, or at which the transfer is to be made out, and it is passed from hand to hand until it reaches the ultimate seller, who saves the intermediate dealers the trouble of handling the stock by delivering both stock and ticket to the original issuer of the latter. On the third day (the settling day or account day) all stock passes and is paid for, and "differences" upon the accounts are settled by means of cheques drawn on "clearing" bankers. 4 INTRODUCTION. Consols have a settlement for themselves at or near the commencement of each month. Day-to-day options are declared at 2*45 P.M., while those done for the current account or for a future account are declared at 12*45 P - M - on ^ e contango day (called also the first making-up day).* Options for future accounts are done, unless other- wise stipulated, at the price of the stock for the account in question, viz., the present market price, plus " contangos " or minus " backwardations.". Thus, if a stock stands at 50, and the estimated rate of interest in contango upon that stock is 4%, we must add on ?T of 4%, if dealing for three accounts ahead, bringing the price up to, say, 50^, or A of 4%, for six ac- counts ahead, bringing it up to, say, 503-, and so on. In the case of a "back," the estimated amount of backwardation for the future period would be deducted from the present price when fixing the option price for that period. Apart from the question of rates, options are fre- quently done at prices considerably above or below the actual prices t for the period in question, and in the examples given of these " fancy " Options, we shall describe the difference between the market price and * The first making-up day for mining shares falls on the day before the contango day for foreign stocks, i.e., three days before the pay day. t It is usual to speak of the ordinary market price for a for- ward bargain in firm stock as the " right " price for the period in question. INTRODUCTION. 5 the price fixed as the " distance". The French term " e"cart " expresses the " distance " plus the amount of option money given ; thus i% given at a price which is y/ over the market price would be an ecart of i%, of which i% is the Option money (i J e"cart, dont i). CHAPTER II. DEFINITIONS. Option. THE word ''option" in connection with transactions in stocks and shares, means a right to buy or sell a certain quantity of stock on a given day, at a price agreed upon at the time the bargain is struck, for which right the "giver" of option money pays a consideration to the " taker " ; the said option money being payable at the end of the stipulated option period. The payment of option money may purchase the right : Call. First, to buy stock at a given price, at a specified future date, this option being known as a " call ". At the end of the option period, the "giver" declares whether he will exercise his option and call the stock or not.* p ut . Secondly, to sell stock at a given price at a spe- cified future date ; the option is then called a " put ". When the option expires, the " giver " tells the * In actual practice, the formal declaration of an option only takes place when the market price at option time is so close to the agreed price of the option that the bargain does not speak for itself. When the market price of the stock is distinctly above or below, it is understood by the "taker" that the stock is bought, or sold, as the case may be. DEFINITIONS. 7 " taker" whether he wishes to put the stock on him at the agreed price, or not. Thirdly, to either buy or sell (whichever may suit Put-and- the " giver ") stock at a prescribed price at a specified CaU " future date ; the name of this double option is the "put-and-call".* The enjoyment of the double right costs twice as much as the single option to buy or to sell would have done. There are, however, exceptional circumstances where, through great scarcity of stock, or dearness of money, the double option, or "put-and-call," can be done more easily than the single option ; in such cases the "put-and-call" money might not be quite as much as double the charge for the single option. An example of this is given in a future chapter. The premium paid for the right of calling or caiio'More. putting stock at some future date, at a stipulated price, is sometimes included in the price at which a transaction is done, for the same date, in firm stock. Thus, a " giver " of option money will buy a certain amount of stock firm for delivery, e.g., two months ahead, at a figure sufficiently over the current market price for that period to carry with it the option of calling a like amount at the same price. This trans- action in options is known as buying stock " call of more ". The "put of more" is the same kind of optional puto' More transaction, in the other direction. The giver sells * In writing this term it is customary to abbreviate it into p.a.c. DEFINITIONS. stock to the taker under the market price with the privilege of being able to sell him another like quan- tity of the stock at the same price at the end of the option period. In these cases, the difference allowed between the market price and the price fixed upon is regulated by the market value of the option in question at the time of dealing, and is fully explained in chapter vii. A stock may be bought call o' more or bought put o' more: in the former case the buyer is "giving option money," and in the latter he is "taking option money". In like manner if A sells to B stock call o' more, the option to call rests with B, and A is "taking option money". If A sells stock to B put o' more, he is giving the option money and has the right to put on B. The price given for the firm stock may carry the right to buy twice, three times, or any number of times, the amount of the firm stock dealt in ; the options being termed "call of twice more," "call of three times more," etc., or, in the selling direction, " put of twice more," "put of three times more," etc. Such fancy options, however, are not very frequently in- dulged in. It may be worthy of remark that " calls " are more often dealt in than u puts," the reason probably being that the majority of " punters " in stocks and shares are more inclined to look at the bright side of things, and therefore more often " see " a rise than a fall in prices. DEFINITIONS. 9 This special inclination to buy " calls " and to leave "puts" severely alone does not, however, tend to make " calls " dear and "puts " cheap, for it will be shown in a later chapter that the adroit dealer in options can convert a "put" into a "call, "a "call" into a "put," a "call o' more" into a " put-and-call," in fact, any option into another, by dealing against it in the stock. We may therefore assume, with tolerable accuracy, that the call of a stock at any moment costs the same as the put of that stock, and half as much as the put-and-call ; the causes referred to on page 7 being the only ones which would be likely to bring about an exception to this rule, and even then the difference would seldom be important. 10 CHAPTER III. WORKING THE SINGLE OPTION. HAVING discussed option dealing in a general sense, we will now pass on to some practical examples of "calls," "puts," and " put-and-calls," explaining how, in some cases, a favourable movement in the market price can be turned to advantage by a giver of option money, and showing the manner in which such deal- ings are booked. All the examples given have been based upon actual market movements, between the years 1888 and 1894, but it is of course understood that the amount of option money quoted is only approximately the market value of the option at the dates mentioned. 9th May, 1892, given 2f % call 10,000 Brigh- ton "A" at 152J for end June. 28th May, sold 5000 Brighton "A" at 157 end June. The giver here sells half his option stock for the end of June, avoids carrying over a " bear" position for two accounts, and secures 4J-/ on ^5000 stock equal to 2iV/o on ; 1 0,000. His position now is that whatever Brightens go to, he can only lose f/ on ^5000, or A7o on ; 1 0,000 ; for if they go higher he can secure his profit on the remaining ^5000; and if they fall below his option price (152!-) he can rebuy the ^5000 sold and abandon his option ; the whole -f/o would be lost only WORKING THE SINGLE OPTION. II in the event of their being quoted exactly 1 52^- at the end of June, when he would call only the 5000 he has sold and lose the difference of rV on , 10,000, or f on ^5000. At the end of June, however, Brighton A are quoted I58f, at which price he sells the remaining ^5000, and the account stands thus : End June, 1892, Account. gth May. To 2$ call 10,000 B. A, at 152$ - --- 237 10 o i^th June. To called lo/m B. A, 152^ 15,28? 10 o Balance - - 243 15 o 28th May. By 5000 B. A, at 157 (sold) 7850 o o 2$th June. By 5000 B. A, at 158! - 7918 15 o 15,768 15 o 15,768 15 o Balance of profit - 243 15 o = 2 T v% on 10,000. We will now take a case which works out less favourably to the giver : 13th August, 1892, given 37, call 4000 Brighton A at 158i end October. By 3rd September the price has risen to 162, but our giver "seeing" a further rise does not sell against his option. If he sold the whole ^"4000 at this price he would obviously secure a profit of f / on the ^4000, as they "stand him in" at 161 J, including option money. If he sold half (say ^2000) he would secure 3f / gross on ^"2000 = i-J7o on ^4000, so that his loss would be limited to iJ7o on ^4000, and he might have a profit in the event of either a further rise or a considerable fall, for if the price at end of October is below 158^, he would repurchase the ^2000 and abandon the call. He does nothing, however, and the price goes 12 WORKING THE SINGLE OPTION. steadily back, until at the end of October Brighton " A's" have run down to 153!-, and his account shows only the option money to his debit : End October Account. i^th August, 1892. To 3% call 4000 B. A, at I58J - --- 120 o We will now take the case of a giver for the put of Spanish 4% Bonds, who prefers covering the whole position at one price. 26th September, 1891, given 1J% put of 5000 (4761 10s.*) Spanish at 71f (cum dividend) end November. On ist October Spanish are quoted /of "ex divi- dend " (the quarterly dividend of i%). This i% taken off the price is no source of profit to the " bear," or the buyer of the put, for it will be debited to him if he puts the stock, the dividend belonging to the person on whom he/&y it. By the 24th October Spanish Bonds are quoted 65-! ; still the giver will not buy against his option, although he could secure 4% net profit by so * The nominal " one thousand Spanish 4% " is a bond of the denomination of 952 6s. This was arrived at at the time of the issue by converting the 24,000 pesetas or francs into sterling at the fixed exchange of 25-20^, and then adjusting the amount of s. d. to the nearest amount which was divisible by 24, without making fractions of pence. Thus 1000 pesetas or francs Spanish 4% is 39 I 3 S - 7^ nominal. These twenty-fourth parts are known as " halfpence of Spanish," the whole 952 6s. being called " a shilling". In the Paris market the nominal thousand Spanish is 1000 francs Rente (4% on fcs. 25,000), so that the " one" Spanish French amount is "a shilling and a halfpenny" English; ten thousand Spanish French amount is " ten and fivepence " English, and so on. WORKING THE SINGLE OPTION. 13 doing (i.e., the difference between 65! and 71} 1% div. - i J option money). If he bought back half his stock at 65f x. d., i.e., 5-^ below his option price, he would be in this position : having secured 5^- on one half, equal to 2rV on the whole, he would in any case make a profit of 2-nr- ij- = irV on the 5000, and stand to make an additional profit on the other half of whatever Spanish were over or under yof x. d. at the end of November But he fancies the next coupon will not be met, and is determined to run his option for all it is worth. Accordingly, on the contango day of the end of November account, he takes a profit on his put of 5-5-% by buying back his ^5000 Spanish at 64!", and putting them at /if cum div. The option is recorded in the ledger as follows : 26th September. To ij% put 5000* (4761 IDS.) Spanish at 7 if - - - 53 n 4 2$th November. To 5 Spanish (bought 64^) - 3053 6 3 To i% dividend on do. (tax not reckoned) - - - 47 12 4 Balance - - - 261 17 7 34i 6 7 6 2$th November. By 5 Spanish (put) at 71^ - 3416 7 6 Balance - - - 261 17 = 54% on 4761 IDS. Subjoined are examples of a successful call and an unsuccessful put of Rio Tinto Copper Shares, in which a very large option business has from time to time been done. On 22nd March, 1890, when Rio Tinto Shares have been steadily recovering some of the enormous fall result- ing from the collapse of the copper corner of the previous year, our operator " sees " a further advance, and 14 WORKING THE SINGLE OPTION. Gives 1A per share call 200 Rio Tinto at 15| for end June Account. The price fluctuates within narrow limits for several weeks, and by 26th April Rio Tinto are negotiable at 16^. To sell at this price would not cover the option money risked ; therefore, as the option has still two months to run, and copper is rising steadily, our giver waits off. The following two weeks witness a remarkable rise, and on 10th May he sells 50 shares at 17f per end June. If he sold for the current account, he would have a " bear " position in 50 shares to carry over three accounts (mid May, end May, mid June), so he pre- fers to sell for the same date as that for which the option is done. This is, in most cases, the simplest and best way of dealing against a future option. On 17th May he sells another 50 shares at 18f per end June, He has now sold 100 shares at a price averaging 18^ against his call at 15!-, and has thus secured a difference of 2f per share on one half of his option, equal to i^ upon the whole 200. But he has only risked i^ originally; therefore, whatever becomes of Rio Tinto, he cannot lose. Let us now examine what his position is. He has risked i^ in option money, to counterbalance which he has, by selling half his stock, assured himself of a margin equal to i^ on the entire 200 shares, and he still has 100 not realised. Whatever he can sell the remaining 100 at, over 15^, WORKING THE SINGLE OPTION. must be net profit. If Rio Tinto stand at exactly 15!- at the end of June, he can make nothing out of the remaining 100. But if they happen to be below i5j he will abandon his call and purchase in the market the shares he sold at i8J average, in which case he will again make on 100 shares the difference between 15!- and the price he buys them at. He practically has a call of 100 at 15^ for nothing, and a put of 100 at I5-J for nothing (since all below 15-! is his profit on 100); or, to use a professional term, he has given O for the put-and-call of 100 Rio at 15^. The conversion of a single into a double option thus exemplified is one of the most important features in option dealing, and the principle is furtherexplained in chapter vi. To follow this option to its successful close we must observe that on 7th June " Rio" are quoted 22^- (ex dividend of io/-), and at this price the giver, having had an exceptional run for his option money, sells the remaining 100, making upon them the whole differ- ence between 15!- and 22^, and taking the dividend of io/- on 100 shares as well. End June Account. 22iid March. To ly'V call 200 Rio Tinto, 15! 237 io o (end June) 2Sth June. To called 200 Rio Tinto, 15! 3175 o o Balance 675 o o 4087 io o loth May. By 50 Rio 'Tinto (sold), 17!- 893 15 o ijth May. By 50 Rio Tinto (sold), i8| - 931 5 o jth June. By 100 Rio Tinto (sold), 22^ x.d. .... 2212 io o By io/- div. on 100 - - 50 o o 4087 io o Balance of profit - 675 o o = 6% on 100 = 3f on 200 shares. 16 WORKING THE SINGLE OPTION. A few days after the close of this successful opera- tion Rio Tinto have advanced still further to about 23, and thinking the price now high enough the operator turns round on the " bear tack," and on 5th July, 1890, gives If put of 100 Rio Tintos at 23i end August. In the former option we saw that he was able to do a three months' call of 200 shares at ITS- per share. The upward movement has been so rapid since then, and takers of option money have had such a bad time in Tintos, that he now has to pay considerably more for a two months' put than he had before for a call three months ahead. His view would appear to be right, when, on the iQth July, Tintos have run back to 22^-. If he now buys the 100 shares at 22yV for end August he can save *- of his option money, and in the event of the price being, at the end of August, First, below 23^, he puts them and loses if - If = T V Second, exactly 23^-, he puts them and loses T \. Third, above 23^, he abandons the put and sells his 100 shares, the difference over -2$\ going to reduce the above-mentioned loss of ^ : if he can get T 9 F over 23^-, i.e., 2311, he comes out of the transaction "even," thus i oo shares bought 2 2TF) Difference if, the same as 100 do. sold 23^) the option money risked, and anything higher than that is his profit on 100 shares. We saw in the last example how the operator by selling one-half of his stock against a call practically WORKING THE SINGLE OPTION. \J got a put-and-call of one-half the original amount of stock. In this example we find that our giver, if he bought back all his stock against the put, would practi- cally have a call of the same number of shares. This operation is known as turning a put into a call, and will be further analysed in a later chapter. On 26th July the shares have risen again to 22^-, only to react by the following week to 22. Once more the giver would have a chance to save a good deal of the option money (23^ 22 = ij) but he does not like to lose even the difference between if and.ij-. He therefore holds out for a further fall, which, how- ever, does not come during the run of his option ; for on the 9th August Rio Tinto are 22, on the i6th August 23 T V, on the 23rd August 24^, and three days later his option expires at 12 '45 on the contango day, shares changing hands at 24^. The option money is consequently a total loss. End Aiigust, 1890, Account. 5th July. To i put 100 Rio Tinto, 23^ 137 10 o 18 CHAPTER IV. WORKING THE DOUBLE OPTION. IN the preceding examples the giver of option money has been made to take a view for the rise or fall of a certain stock, and to base upon this view an operation in the single option. Now, it frequently happens that a giver, wishing to do an option, is undecided as to the direction which the next few points move will take in the stock under consideration, so he commences operations by giving for the put-and-call of the stock and waits for further developments. This, by the way, frequently turns out to be a judicious mode of pro- cedure, especially when the object of the speculator's attention happens to be one of the American Railroad Stocks, in which the fluctuations are generally violent and uncertain. The American market has for many years offered a fair field alike for the giver and for the taker of option money, both parties to the deal in a three months' option having, as a rule, plenty of ex- citement for the money! Indeed, it is surprising that so many speculators in American shares should con- tinue to deal in "firm" stock, when so much amuse- ment can be procured at the moderate prices generally ruling for American options. A giver of option money on Americans once observed : " If only I had WORKING THE DOUBLE OPTION. 19 given for the put as often as I have given for the call, how much money I should have made and how little I should have risked!" It is more than likely that if this operator had nerved himself at the time to pay twice as much for the put-and-call as he paid for the single option, he would, in the long run, have had little reason for regret. Let us illustrate our subject by a put-and-call of Louisville and Nashville Railroad Shares. * 2nd January, 1892, given $5J per share put-and-call 200 Louisville at 86| end March. This looks a lot of money to give in a quiet mar- ket, but option takers have unpleasant recollections of rapid and unforeseen movements in the leading specu- lative American shares. They cannot forget the bad * American Railroad Stocks dealt in here are in shares of ftioo each (except Pennsylvania Shares and Philadelphia and Reading Shares, which are of #50 each). The nominal amount of stock, in dollars, of 100 shares is therefore $10,000, which at the nominal or fixed exchange of $5 to i is 2000. The price quoted in London is arrived at by converting the New York price per cent, into an English price per cent, at the exchange of the day. The English price is therefore in s. per cent. : thus, $97% New York at $4.85 is "100% London, so that if one bought 100 shares (= $10,000) in New York at 97 (= $9700) and sold 2000 (nominal) in London at 100 (= 2000), the proceeds of the London sale at the exchange of $4.85 would yield $9700 to pay for the purchase in New York. But it is more convenient and therefore customary to speak of 50 shares or 100 shares in the London market, and regard the price quoted as a sort of English dollar (4/-) price. The above option example is accord- ingly expressed, " given $5^ put-and-call of 200 shares," but, correctly speaking, it would be 5 |% put-and-call of "4000 stock. 20 WORKING THE DOUBLE OPTION. turn Louisville did them in October and November, 1890, by dropping 16 points in half as many weeks, only to catch them " out " again the following autumn, when the same shares rushed up from 68 to 8 rj in less than two months. By 1 6th January Louisville are quoted 81^ (ex dividend $2^-). In comparing the market price with the option price the giver has now always to take into consideration the dividend ; if he puts the shares the taker will debit him with the dividend ; if he calls them, he will receive it from the taker. In other words, he will/z*/ the stock if it stands below 86f - 2 1 = 83!"' or call it if it is quoted above that figure. It is usual to say the option price is 83 J x.d. The shares are now a weak market, and the giver decides to go with the tendency, and refrain from buy- ing until his option money is covered. 2 jrd January, Louisville 79^. If he bought 200 shares at this price he would make $4f, and lose $5^, i.e., $J on balance. On joth January they are down to /6-f. Now is his chance. On 30th January he buys 200 Louisville at 76 J per end March. This not only covers his $5^ put and call money, but leaves a profit of $i-J per share as well, and there is the chance that he might make still more during the two months the option has yet to run. He cannot make more if the shares continue to fall in that case he has closed his position too soon, and missed a further WORKING THE DOUBLE OPTION. 21 chance of profit. Nor can he secure any additional advantage by an advance in price to 83^ x.d. (his option price), unless, indeed, he has the luck to hit off a reaction in selling out again and covering with a pro- fit ; but it must not be forgotten that in selling again under the price at which he has the right to put he risks losing part or all of the profit he has already secured. His only chance of more profit without risk- ing anything is for Louisville to rise above 83-! in the next two months. What is his position then ? We will leave out the i-J realised profit, and consider it put away for some future enterprise. By his purchase of 200 shares he has covered the original risk of $5 J, but if the price is over 83!- at the end of March he will not put these 200; on the contrary, he will exercise the other part of his option, viz.> call 200 shares, and thus be in the position of having 400 shares to sell. Then his additional profit will be the difference on 400 shares between 83! and whatever they fetch. Now, this is equivalent to saying that he has a call of 400 shares at 83!- for nothing. So he has, and the operation is known as " turning a put-and- call into a call " by buying all the shares. Just as in the example on page 15, we saw that the giver for the call of 200 Rio Tintos practically became the possessor of the put-and-call of one half the amount, so we find now that the giver for the put-and- call of 200 Louisville is able to turn his option into a call of twice the number. To return to the subject of this example, Louis- 22 WORKING THE DOUBLE OPTION. villes have no recovery in them beyond reacting to 78 on 1 3th February, and at the expiry of the option on contango day, at the end of March, the price has fallen to 75^-: the ledger shows the following entries : 2nd January, 1892. To $5^ p.a.c. 200 L. and N. at 86 - - - 205 o o $oth January. To 200 L. N. at y6 x.d. - 3075 o o (bought) To $2^ div. on 200 shares - 100 o o Balance ... 75 o o 3455 2-jth March, 1892. By 200 Lou. N. at 86f (put) 3455 3455 Balance of profit - (i on 200 shares.) The following shows a put-and-call of Chicago. Milwaukee, and St. Paul Shares which leaves a small margin of profit to the taker of the option money, and is therefore unprofitable to the giver.* 2nd May, 1891, given $4i put-and-call 100 Milwaukee at 66| end June. We will suppose, in this case, that the giver is really in favour of a rise in Milwaukee Shares, but having often been mistaken before when he has "seen " a rise, he this time secures a put and call on not too onerous terms, and hopes to be able to do what we illustrated in a former example, i.e., cover his risk by buying his 100 shares $4^ lower than his option price. Then, if within the two months his * It is not unusual for both giver and taker to make a profit out of an option, as, on the one hand the eventual difference in price may still leave a margin of profit to the taker of option money, and on the other the giver, under the protection of his option, may have "jobbed in and out" several times,' and ulti- mately have secured more than he originally risked. WORKING THE DOUBLE OPTION. 23 option has to run, Milwaukees rise well over the difference is all his on 200 shares double his original option amount. This speculator is, however, doomed to disappoint- ment, for he has embarked in his enterprise just before a period of unusual inactivity for American shares. The next week Milwaukees are down $i, a fortnight later they are quoted 65-!, only $ij under his option price, yet another week brings merely a niggardly ^ move, and so on until at the very end of his term the price has barely managed to drop to 63%. He buys the 100 shares so, and puts them at 66f, saving $3 only out of the $4^ risked. His account shows his loss thus : 2nd May, 1891. To $4$ p.a.c. 100 Milwaukees at 2-jth June. To 100 Milwaukees at 63! - 1275 (bought) 1360 o o 2"jth June. By 100 Milwaukees at 66f - 1335 (put) By Balance - - 25 o o "1360 Balance - ... 25 o o. j (ij loss on 100 shares.) This $ij on 100 shares is the profit to the taker of the money, unless he has jobbed against the option. The next is an example of a put-and-call of New York Lake Erie and Western Shares, where the giver manages to make a profit by dealing in the shares under the cover of his option, although the ulti- mate price shows a margin of profit to the taker. 9th July, 1892, given S2f put-and-call 500 Erie at 26J end September. Eries having been on the down grade all the year 24 WORKING THE DOUBLE OPTION. (the price in the preceding January was about 35), the buyer of the put-and-call thinks there may be a reaction which will give him an opportunity of selling his shares and going for a further fall. His chance comes a month later. On 6th August he sells 500 Eries at 29f per end September. This is $2f above his option price, so, if Eries con- tinue to rise, he only stands to lose J. On the other hand, if they fall considerably, say below his option price, he stands to make a profit on the 500 he has sold, and the 500 he will put. In other words, for the risk of \ on 500 (= yV on 1000) he has the put of 1000 shares at his option price, or, as a dealer would express it, he has given TG for the put of 1000 Eries at 26J. This would be a case of turning a put-and- call into a put by selling all the shares. His view proves to be correct, and the following week Eries are 28f. He resolves to run the speculation until he can buy back under his option price, which he eventually succeeds in doing, for on 9th September he buys 500 Eries at 25f per end September. He has secured $4^- on 500 shares, i.e, his 2% option money and a profit of $i| besides. He is " even " in the shares, he has a profit of if on 500 shares, and his original put-and-call for nothing. At the end of September he will make an additional profit of what- ever Eries are over or under 26|, and thus his circumstances are very comfortable. WORKING THE DOUBLE OPTION. As a matter of fact, at the end of his time Eries are 26^ (only f below his option price a very lucky quotation for the dealer who ran the risk of the option, i.e., the taker of the option money, who makes the difference between 2-J option money and f loss, unless indeed he has spoilt it by dealing in the stock), and the fortunate giver buys again 500 shares at 26^-, which he puts at 26-|. The transaction is thus stated in the " giver's " ledger : End September, 1892, Account. gth July. To $2j p.a.c. 500 Eries at 287 10 o (bought) 2537 10 o gth September. To 500 Eries at 2f 2"jth September. To 500 Eries at 26^ (bought) 2650 o o To Balance -" - - 175 o o 5650 o o 6th August. By 500 Eries at 2g| (sold) -2962 10 27 th September. By 500 Eries at 26$ (put) - 2687 10 5650 o Balance of profit - 175 o i| + | = if on 500 shares. The taker's ledger would show his profit thus, if he had run his option until the last moment without dealing against it : End September, 1892, Account. 27th September. To 500 Eries (put at Balance 2687 10 o 250 o o gth yuly. By $af p.a.c. 500 Eries at 26$ 287 10 27 1 h September. By 500 Eries at 26^ (sold) - 2650 o 2937 I0 250 o Balance of profit $2^ on 500 shares. 26 CHAPTER V. THE CONVERSION OF OPTIONS. THE arguments employed in the eight foregoing examples of optional dealings will lead the giver of option money to the following conclusions : 1. That a call of a certain amount of stock can be converted into a put-and-call of half as much by selling one-half of the original amount. 2. That a put of a certain amount of stock can be turned into a put-and-call of half as much by buying one-half of the original amount. 3. That a call can be turned into a put by selling all the stock. 4. That a put can be turned into a call by buying all the stock. 5 and 6. That a put-and-call of a certain amount of stock can be turned into either a put of twice as much by selling the whole amount, or into a call of twice as much by buying the whole amount. We must now inquire to what extent the original option money is affected by these hedging operations in the firm stock, and whether the option price moves or remains always the same. For this purpose let us take a simple example for each of the six cases above mentioned, it being understood that the bargains in firm stock are effected for the same date as that for which the option is done. THE CONVERSION OF OPTIONS. 2/ Example i. Given 1% call ^2000 stock at 80. Sold ^"1000 80. At the end of the time, if the stock stands at 82, ^2000 is called, of which ^1000 is already sold at the option price ; the other ^"1000 can be sold at 2% profit, which equalises the i% on ^2000. Anything over 82 would be profit on ^"1000. If the stock stands at 78 the call is abandoned, the " bear" of ^1000 is bought back at 78, and the 2% on ;iooo again pays the \% option money on ^2000. Anything below 78 is profit on ^"1000; the position therefore can be expressed as : given 2% put-and-call of i ooo at 80. Hence we are able to formulate the following rule : To sell half the stock at the option price against a call is equi- valent to giving twice the amount of money for the put-and-call of half the quantity of stock at the same price. Example 2. The second example may, by way of variation, be explained by combining the single option given with the double option taken, thus : Given \% put of ^2000 stock at 80. Bought ^"1000 ,, 80. Then to close the operation Taken 2% put-and-call ^"1000 at 80. Whatever may be the price of the stock at the end of the option period, the operator is "even". He has neither profit nor loss ; for, firstly, if the stock has risen, 28 THE CONVERSION OF OPTIONS. say, to 90, he abandons the put of .2000 at 80, the ,1000 stock bought at 80 is called of him at the same price, and the amount of option money given and received is the same. Secondly. If the stock is quoted, say, 70 Then he puts 2000 at 80. He has bought ,1000 at 80 ; and is obliged to buy /iooo at 80, which is piit on him, the option money given and received again balancing. The following rule is established from this ex- ample : If option money is given for the put, and half the amount of stock is bought against it at the option price, the dealer has practically given twice the option money for the put-and-call of half the stock at the same price. Example j. A gives i% call of .2000 stock at 80 ; And sells ^2000 ,, 80. B gives i% put of ^2000 ,, 80. If the stock is over 80 at the expiry of the option, A calls the ^2000 he has sold at the same price and loses exactly the option money (\% on ^2000). B abandons the put and loses i%on 2000. If, on the contrary, the stock is below 80, A abandons the call and secures as much as he can on the ^"2000 sold, anything below 79 (i.e., 80 - i% money) being his pro- fit on ^"2000. B exercises his put, and also benefits on ^"2000 to the extent of any difference below 80 - 1%. We see THE CONVERSION OF OPTIONS. 29 therefore that whichever way the price goes the positions of A and B are identical, and our deduc- tion is : If all the stock is sold by the giver against a call at the option price, it is equivalent to giving the same option money for the put of the same amount of stock at the same price. Example 4. Given i% put ^2000 stock at 80. Bought ^"2000 ,, 80. If the stock stands below 80 when the option ex- pires, the ^"2000 bought at 80 are put at 80, and the option money is lost. If it stands over 80 the put is abandoned, and a profit is made on the ^2000 bought ; the profit begins at 80 + 1% = 81 ; this is the same thing as if the giver had bought the call of ,2000 at i% instead of the put, and establishes the next rule, viz. : If a giver of money for the put buys the whole of the stock at the option price, he converts his operation into giving the same amount of money for the call of the whole amount of stock at the option price. The $th and 6th cases are too obvious to need illus- tration after the above examples, for it follows by in- version that if a call can be turned into a put-and-call of half the amount by selling half the stock, this same put-and-call can be converted into a call of twice the amount by buying all the stock ; the option money is first doubled and then halved, and the option price always remains the same. The preceding examples have all been treated from the giver's point of view. It need hardly be men- 3O THE CONVERSION OF OPTIONS. tioned that the principle remains the same whether the money is given or taken, only, when looking at it from the taker's side, the operation in the stock must be reversed. For instance, a taker for the call wishing to convert his option into the put-and-call, buys half the amount ; and a taker of the put-and-call sells the whole of the stock in order to convert the operation into taking for the call of twice the amount, but buys the whole when he wishes to turn it into taking for the/#/ of twice the amount, etc. CHAPTER VI. THE PRINCIPLES FORMULATED. HAVING propounded the six principal rules of option dealing, it remains now to be shown how the option money is affected by dealing in the stock at a different price from that at which the option has been fixed. We know that a giver for the call converts his option into twice as much money for the put-and-call of half the amount of stock, if he sells half at the option price. Now, at whatever price he sells half the stock, he still converts his option into a put-and-call at the original option price, but the amount of money staked is in- creased or diminished according as he sells the stock under or over the option price. It will not be necessary to give illustrations in each of the six examples considered in the last chapter, as the principle which we propose now to discuss applies equally to all optional dealing. Firstly* Selling against a call over the option price. Given i% call ^"2000 stock at 80. Sold .1000 ,, 8o|-. * The illustration is in each case regarded from the giver's point of view. 32 THE PRINCIPLES FORMULATED. If the stock stands higher than 80 at the maturity of the option the ,2000 will be called. \% has pre- viously been secured on ^"1000, so that the other ,1000 must be sold i \% above the option price (viz., 8iJ) to cover the option money ; anything over 8i is profit on ^"1000. If the stock stands below 80 the call is abandoned, and the repurchase of the ^"1000 at ij% under the option price (viz., 78 J) will cover the option money, anything below that being profit on /i ooo. Obviously the same result would follow if the giver paid iffi put-and-call of ^"1000 stock at 80. Hence we derive the following principle : ff a call is turned into a put-and-call by selling half the stock over the option price, the put-and-call money is LESS than double the call money by exactly the difference betwten the option price and the sale price. This difference we shall call the " distance," and adopting the symbols C = call money ; p.a.c. = put-and-call money ; P = put money ; D = distance, the principle may be thus formulated P.a.c. (given) = 2C (given) D. From the giver's point of view this " distance " is favourable, for he sells over the option price. The formula would remain the same from the taker's point of view, but in that case the " distance " would be unfavourable, seeing that he buys half the stock over the option price. THE PRINCIPLES FORMULATED. 33 Secondly. Selling against a call under the option price. Given i% call ^"2000 stock at 80. Sold ^1000 ,, 79. It will be readily seen that if the stock at the end of the time is over 80, the ^"1000 hitherto unsold must fetch 83, in order to cover the i% loss on ^1000 and the 1% option money on ^2000. On the other hand, should the call be abandoned, the ^1000 must be repurchased at 77, in order to pay the i% risked on ^2000. In the first case, the difference over 83, and in the second case, the difference below 77, is profit on the ^1000, which again is equivalent to the expression, " given 3% put-and-call of ^1000 stock at 80 ; " and so we obtain our next rule, viz. ; If a call is turned into a put-and-call by selling half the stock under the option price, the put-and-call money is GREATER than double the call money by exactly the "distance" or difference between the option price and the sale price. Here is the formula : P.a.c. given = 2C given + D. In reckoning the amount of option money involved, when converting any one option into another, it will be necessary to consider always whether the " distance " is favourable or unfavourable. The terms are naturally reversed when the giver's and taker's positions are compared. In like manner, in turning a put into a put- and-call, a purchase of half the stock above the option 34 THE PRINCIPLES FORMULATED. price involves an unfavourable "distance," and may be expressed P.a.c. (given) = 2? (given) + D. On the other hand, a purchase of half the stock below the option price ensures a favourable " distance," and diminishes the risk of the giver P.a.c. = 2? - D. Again, from the taker's point of view, the "distances" are reversed, as he has to do the opposite transaction to that of the giver ; therefore, in the two last formulae + D is unfavourable to the giver but favourable to the taker, and D is unfavourable to the taker but favour- able to the giver. It is easy to deduce from the above examples the necessary formula for the conversion of any other option by substituting + D for D and vice versa when the sense of the " distance " is changed by selling instead of buying, or by buying instead of selling : thus, if we wish to turn a put-and-call into a call by buying all the stock above the option price, we know- that the distance in this case is unfavourable, and that P.a.c = 2C -f or - D ; therefore 2C given = p.a.c. given + D (unfavourable), and C = p.a.c. + D 2 Example. Given 3i% put-and-call of 1000 stock at 80. Bought 1000 stock at 8U. How can this be expressed in one term ? We know that the put-and-call is turned into the THE PRINCIPLES FORMULATED. 35 call of ^2000 at 80 ; it only remains to be shown how much option money is involved. Formula : _ p.a.c. + D The present operation may therefore be expressed Given 2 % call of 2000 at 80. Again, if a put-and-call be converted into a put of double the amount by selling all the stock above the option price, the distance here is favourable, and we know already that P.a.c. = 2? + or - D 2 P (given) = p.a.c. (given) - D (favourable), therefore P = p.a.c. D 2 Example. Given 2J% p.a.c. 1000 stock at 80. Sold 1000 stock at 81. What is the equivalent of this operation in one term ? Formula : p _ P- a - c ~ D 2 = 3. o/ 4/0 The equivalent in one term is therefore Given f% put of 2000 at 80. The utility of the above formulae becomes more apparent when it is proposed to give or take option 36 THE PRINCIPLES FORMULATED. money at a price other than the market price of firm stock for the term in question. For example, the call of a certain stock at 80 for a fixed period is i \% ; what would the call be worth for the same period (i) at SoJ- ; (2)at 79 |? Before discussing this point, it is necessary to ob- serve that the put-and-call money on a stock for a given period would be the same, whether the actual market price for the period or a price a little different be stipulated, providing that the difference does not bear any considerable proportion to the whole amount of the put and call money involved. Indeed, it might suit a taker better to fix a price rather above or below the actual market price for the period. It is difficult to define how far this difference may go without affecting the premium, but it is fairly safe to say that no ap- preciable difference would be made if the "distance" did not exceed one-fourth part of the put-and-call money. The reason is not far to seek. If a taker is willing to run the risk of a fluctuation of a stock from 80 for 3%, he would also be willing to fix, say, 8oJ, as he would gain in the event of a rise exactly as much as he would lose in the case of a fall, and he does not begin his optional transaction with any considerable portion of his option money " run off". Further, in nearly every instance in active speculative stocks, the chance of a rise or a fall is, to borrow a sporting expression, " even money betting ". To return to our examples : The call at 80 costs THE PRINCIPLES FORMULATED. 37 i J%. What is the call worth at 80 J ? Now, we assume that p.a.c. at 80 = p.a.c. at 8o|- ; we know that the call must cost less at 8o|- than at 80 ; the formula therefore is Again, what is the cost of the call at 79! when the right price is 80 and the put-and-call 3% ? The ''distance" is unfavourable here to the option money risked. The formula therefore is p.a.c. + D 3+i. 2 2 '* So we see that if a stock stands at 80, and the put- and-call is 3% for a certain period at 80 The call at 79} would cost if, at 80 4, n atSol if, and so on, the difference in the call money being always one-half of the "distance," or, to express it in another way, in giving for the call you deduct from the call money half as much as you add on to the price, or add on to the call money half as much as you take off the price. This conclusion can also be arrived at with- out examples by the use of our formulae : p.a.c. D and C 1 = - 38 THE PRINCIPLES FORMULATED. That is, twice the difference in the option money is equal to the "distance". It is quite usual for options to be done for long periods, e.g., three months ahead, where the price fixed is considerably above or below the " right" price for the period ; in these cases the call money is arranged on the basis of a put-and-call increased by an arbitrary amount calculated to cover the additional risk involved in taking option money with so much of the money already "run off" in one direction. For example, the call of Milwaukees at the actual price of 65 for three months is, say, $2 J ; that would make the put-and-call at 65 worth $5. If the giver wishes to risk $i for the call, what price must he fix to do his business? If the put-and-call at both prices were equal, the answer would be D - 2 (C - C 1 ) --.-*) Distance = $3 over the price. Now, a dealer would not, as a rule, care to take $5 put-and-call of Milwaukee $3 over the right price, although the risk may be said to cut both ways. Milwaukee would have to rise from 65 to 73 before the taker would lose, and in the other direction his loss would begin proportionately sooner, viz., after a $2 fall to 63 ; the range of his risk, or, as the Americans call it, his " ten dollar straddle," would be from 63 to 73 instead of 60 to 70. But one of the reasons of his un- willingness to accept the same terms is that a taker of option money, from the nature of his business, backs THE PRINCIPLES FORMULATED. 39 the inertia of the stock in which he is trading ; just as the giver places his money on the rise or fall, or both. If the stock does not move at all during the run of the option money (an unusual event by the way), the taker who has fixed 65 makes the whole $5, whereas he would only make $2 out of the $5 if he had taken his put-and-call money on the basis of 68. When, therefore, a price is fixed considerably under or over the actual price, the put-and-call is con- sidered to be worth a little more, but the increase in value cannot well be expressed in any fraction of the " distance," or said to bear any particular ratio to the whole of the '' money " ; it is rather a question of indi- vidual fancy at the time of dealing. To come back to our present example : the taker thinks that in dealing about $3 out of the price, he ought to have $5^ p.a.c. instead of $5, so, in answer to the ques- tion, what price must be fixed for Si call of Milwaukees for three months when the right quotation is $5 p.a.c. at 65 and the taker asks S|- more for the additional risk we have recourse to the same formula, C being 2f instead of 2\. D = 2 (C - C 1 ) -a -i) -3i The price to be fixed is accordingly $3^- over the current quotation of 65, or Si call at 68^-. CHAPTER VII. THE CALL O' MORE PUT O' MORE. HAVING now firmly established the principles involved in turning the single into the double option, and vice versa, and having discussed the manner in which the original option money is affected by dealing in the firm stock at the option price, or at any other price, we shall be able to cope easily with the apparent in- tricacies of call o' more and put o' more transactions. We have seen in the chapter on definitions that the call o' more is an option carried in a purchase of firm stock effected at a price which is above the right mar- ket price for the period in question. It now remains to be shown, with the assistance of the principles already laid down, at what prices such transactions should be arranged, given a certain put- and-call value. From its very nature the call o' more or put o' more must of necessity be an optional bargain at a price other than the right price, seeing that the option money is inchided in the price at which the stock is bought or sold. Consequently transactions of this description are not often done for long periods ahead, for the "distance" would become so large that the option would have to be very dear to compensate the taker's THE CALL O' MORE PUT O' MORE. 41 risk in commencing a " long shot " operation with a considerable amount of the money " run off". Call o' more bargains are therefore more freely done from day to day or for a week, one account or one month ahead. We will first follow one of these fancy options through in the manner adopted with the examples given in chapters iii. and iv. On 20th August, 1892, De Beers Shares stand at i4. The three months' call until the middle November account is worth, say, if per share. Our operator "sees his way " to buy 200 De Beers Shares at 15i 3 .a.c. - D _ ; Lli^j Answer, i J put at 79 J. Exercise. Bought ,4000 stock at 80 call o' more. Sold 1000 78. 1000 ,, 78f. 2000 79f. 2000 ,, 8oJ. What single transaction would now make the position even, without profit or loss ? The first ,4000 stock is sold at an average of 78|-. The risk is therefore limited to \\ on ^4000, and can be expressed : Given i^ call ^4000 stock at 80. Now, this is converted into a put-and-call of ^2000 by selling one half the option stock at 8o| P.SLC. - 2C - D -*i-i = 2% * Presuming that p.a.c. at 80 = p.a.c. at 8o|, see page 36. THE CALL O' MORE PUT O' MORE. 47 which can in turn be expressed : Given 2% put-and-call ^2000 stock at 80. The operator must therefore take 2% put-and-call of ^"2000 stock at 80, in order to make himself even without profit or loss. Exercise. (From the taker s point of view.) Bought ^2000 stock at 80 put o' more. Given that this option money has been taken, on the basis of 2 J/ put-and-call, what is the present price of the stock for the period in question ? Now, we know that the stock must stand higher than 80, for the buyer, who is here the taker of option money, has allowed for the option money in the price. , p.a.c. 24- Put o more = = * D = */ Therefore, the stock must now be 8of . Exercise. (From the takers point of view.) Sold ^2000 stock at 80 call o'more, given that the put and call is 3% ; at what price would this dealer buy stock put o'more ? * We must first find the market price of the stock. _ . , p.a.c. Call o more = therefore D = i and the market price must be 79. Now if the stock stands at 79, and the dealer is willing * In this exercise the question of contangoes is not con- sidered. 48 THE CALL O' MORE PUT O' MORE. to take 3/ put-and-call, even if the price fixed is 1% out of the market price, he would also buy the stock put o' .. p.a.c. . more at a distance of = i. Answer, 78. 3 In the introduction, it was stated that the amount of option money involved in a call of more transaction was greater than would appear at first sight to the uninitiated. Take the following illustration : From time to time there have been immense optional trans- actions done in Consols, and at those times the difference between the buying and selling price of ; 1 00,000 consols would seldom exceed J%. Thus, at a given moment we will say Consols are 105! f. An option dealer (not a jobber in the Consol market) is anxious to sell a block of Consols for which he would perhaps be willing to take 105^. As, however, he has a buyer of Consols call o' more, he sells them to him at io5f call o' more for the account ten days ahead. He has apparently only asked the full market turn, and has " thrown in an option ". But on examination it appears otherwise. It would have suited him to sell his Consols at 105^-, but finding a giver of Option money, he charges him 105! call o' more. The seller, from his own point of view, has thus taken ^ call at J above the price equivalent to f put-and-call at 105-! ; which will admit of a fluctuation of f% (from 105^ to 1 06) without causing him loss. Thus a "straddle" of f % seems to be the result of getting instead of giving the turn of the market. 49 CHAPTER VIII. THE CALL OF TWICE MORE, THREE TIMES MORE, ETC. IN doing a call o' more transaction, the price at which the firm stock is bought may carry the right to pur- chase more than an equal amount of the stock at the same price ; it may give the buyer the privilege of calling twice more, three times more, or indeed any number of times more ; but in this country such fancy options are not much done, although in Germany the call of twice more (zweimal nock) is not unfre- quently negotiated. It may, nevertheless, be of interest to give the for- mulae upon which the prices are based for these optional transactions, more especially as the sequence of fractions is somewhat curious and withal easy to remember. Firstly. If a stock stands at 80, at what price ought one to buy it call of twice more, when the put- and-call is 3% ? Now, in this case the "distance" given in the firm stock is to carry a right to call twice the quantity at the whole distance above the price. The 4 5O CALL OF TWICE MORE, THREE TIMES MORE, ETC. option money staked is, therefore, one half of the distance. P.a.c. = 2C + D Now here C = therefore p.a.c. = D + D therefore D - ' ' = f" = J i over tne P r i ce - Answer 81^-. Again, what is the "distance" of a call of three times more? Here the call money is one-third of the "dis- tance " given on three times the amount of stock : P.a.c. = 2C + D here C = 3 therefore p.a.c. = h D O ,55 3 and D . LE^E: 5 Hence if the stock stands at 80, and the put-and-call is 5/ i then the price would be 83 call of three times more. Thus we see that the call of twice more is worth at least over the price, the call of three times more 3 p.a.c. over the price, and by the same process we can ascertain the distance of call of n times more. CALL OF TWICE MORE, THREE TIMES MORE, ETC. 51 P.a.c. = 2C + D. Now C = n therefore p.a.c. = \- D n 2D + nD . r TV * (p.a.c.) therefore D = ^ + g 7 Or, putting it more plainly, the "distance" involved in a call of any number of times more is that fraction of the put-and-call money represented by a numerator equal to the number of times more, and a denominator equal to the same number + 2. To recapitulate Call of more " = over the price. 2 p.a.c. _ p.a.c. ,, twice more 4 2 3 p.a.c. three times more =- 5 .a.c. 2 p.a.c. 6 3 5 p.a.c. five = 6 p.a.c. = 3 p.a.c. six ,, o 8 4 7 p.a.c. seven etc., etc. In practice it would be found that a giver could not as a rule " get on " at the figures obtained by 52 CALL OF TWICE MORE, THREE TIMES MORE, ETC. the preceding formula, for the reason set forth in chapter vi. For instance, supposing a stock is 80 and the put-and-call 4%, then, according to the formula that stock would be worth buying at 83 call of six times more. But what is the taker's position then ? Assuming that he has sold ^1000 stock at 83 call of six times more he must first rebuy the ^"1000 firm at 80 ; he has then taken 3% n ^1000 = J% on ^6000 call at 83. If he now wishes to turn his position into put-and- call He buys ^3000 more at 80, then p.a.c. = 2C + D (favourable to taker) -i+3 = 4% He has taken 4% put-and-call of ^3000 stock with three-fourths of the option money already run off, and has dealt in ^5000 stock firm in order to do it. Pro- bably no dealer would be willing to run such a risk on these terms, viz., on the basis of the current rate for the put-and-call. Exercise. A stock is quoted at 80, and the put-and-call for a certain period is about 2j/ . A is willing to take 2f% put-and-call of the stock at about i J% above the price. B will take 2f/ put-and-call at about iJ/ Q below the price. At what price would a dealer (1) Sell ^2000 call of three times more ; (2) Buy ^2000 put of three times more, to leave himself a profit of \ on the put-and-call ? CALL OF TWICE MORE, THREE TIMES MORE, ETC. 53 And how must he hedge in the firm stock to make himself "even?" (1) If he wants ^ profit he must secure 2^% put- and-call. 11 r i 3 p.a.c. 3 x 2-A- Now call of three times more = Jt - c - = = if- He would therefore sell ^2000 stock at 8i call of three times more, and in order to fix his profit he must first buy ,2000 stock at 80. He then stands thus: Taken 1% ca ^ f ^6000 stock at 8ii Next, by buying ^3000 more at 80, his position is : Taken 2^/ p.a.c. of ^3000 stock at 8 1*. He then gives A 2! p.a.c. of ,3000 stock at 8i. He has thus levelled his position, has secured I profit on ^3000 stock, and in order to accomplish this he has had to buy ^5000 stock (2) In the same manner, r i 3 p.a.c. 3 x 2-t put oi three times more = = = 1-% ; so our dealer would buy ^2000 stock at 78! put of three times more. Then, in order to be able to secure his profit by dealing with B, he first sells at 80 the ,2000 he has bought at 78^. He has thus taken F/ put of ^"6000 stock at 78^. He next sells further ^3000 stock at 80, and his position is, by the formula p.a.c. = 2 P + D : taken 2* p.a.c. of ^3000 at 78i Accordingly, by giving B 2! p.a.c. of .3000 at 787 he secures i profit on ^3000 stock and makes himself " even," the operation having necessitated the sale of ^5000 firm stock. 54 CHAPTER IX. THE SINGLE OPTION DISGUISED. IN all the examples of option dealing considered in former chapters, the operator has been made to deal against his options in firm stock for the option period. In actual practice this is frequently very difficult to do, especially when it is a question of dealing for two or three months ahead in times of excitement and great speculation. At such seasons a buyer of stock for forward delivery would have to make a great conces- sion in the price in return for the convenience of avoiding a difficult contango. Again, it may occur that, on account of some very bad news, a certain stock has been much oversold ; that is to say, many people not possessing any stock themselves, may have sold " bears " of considerable quantities, which, at the following contango day, they must either borrow or buy back. Holders, in such cases, if they lend their stock at all, may demand a "backwardation," of which speculative "bulls" also get the full advantage. In the war scare, some ten years ago, Russian stocks were so freely sold here by "bears" that the German holders were able to exact from J% to i J/ o backwardation per account for the loan of their stock for many months. At that time it would have been more difficult to give THE SINGLE OPTION DISGUISED. 55 for the put of Russian than for the put-and-call for this reason : A taker of option money, as a rule, does not wish to run a single option, for that would be purely a matter of taking a view for the rise or the fall. He likes to turn every single option straight away into a double option, because, in spite of then "standing to be shot at " in both directions, he is covered by twice the amount of option money on half the quantity of stock, and, as we said in a former chapter, he likes to back the inertia of the stock in preference to taking a view of its activity one way or the other. Now, if an option dealer had already taken money freely for the put of Russian stock, and in every case sold one half of the amount for the current account, he would find himself at each settlement a big borrower of stock at a growing backwardation, which was perhaps not allowed for at all at the time of dealing. In such a case, although he might be willing to increase his " book " in the put-and-call, he would be very un- willing to increase his "bear" position in the firm stock. To put it into figures, he would probably say to an intending giver : "I will take 5^% put-and-call of ^5000 stock at 82 for three accounts ahead, but if you want to give for the put I must protect myself and fix either 3^% put at 82, or 2f% at 81 ". An operator, in order to disguise his position and avoid suspicion, may elect to give for the put-and-call of a stock instead of either the call or the put, and afterwards turn his position into the single option by degrees. There is a story of a German banker, 56 THE SINGLE OPTION DISGUISED. anxious to dispose of a large amount of some bank stock, approaching an option dealer who, after some conversation upon the merits of the stock in question, took money from him for the put-and-call of a con- siderable portion of the amount the banker really wished to dispose of. Some little time after the option dealer found that the stock was easier to buy than to sell, and not wishing to have this large block thrown on his hands he took every opportunity of raising the price whenever it could be done at the expense of buying a few thousand pounds more of the stock. A short time before the option became due the selling seemed to have ceased, and, in fact, the price rose so rapidly that the option dealer began to wonder where he would get the balance of stock from in case it was called of him. Indeed, so great was his uneasiness that by degrees he covered the whole of his position, the seller of the stock, unknown to him, being his option giver ; and on the day the option was due, the price was so far above the option price that no doubt was left in his mind as to which way the banker would declare his option. At option time the banker approached the dealer, who said : " I congratulate you on the fine pro- fit you have on your option ; you, of course, call the whole of your amount ". " On the contrary," replied the knowing banker, "I do not call any ; I put it on you." And the operation being well timed, an un- favourable announcement concerning the affairs of the institution was made that afternoon, and the option THE SINGLE OPTION DISGUISED. 57 dealer found himself the unwilling possessor of the whole amount of stock which had belonged to the banker, who throughout the operation had never once been obliged to show his hand. The above anecdote, which is probably fictitious, is not quoted so much with a view to dwell upon the ethics of Stock Exchange transactions as to remind the reader that the apparent market in 100 shares is one thing, and the actual market in 10,000 something very different. CHAPTER X. OPTION-DEALING ABROAD. ALTHOUGH very large transactions are from time to time done on the French and German markets in options, London is par excellence the option market of the world. Perhaps the largest individual transactions have been done in Paris, where speculators occasionally deal in amounts which are almost unheard of on this side ; but there is nowhere the same facility for giving and taking, for operating in long and short options, and for hedging against a favourable put or call in the firm stock as that which exists in London. It rarely happens that an option is done in the Paris market for more than one month ahead, and in Berlin too the majority of such dealings are arranged for a similar period. In London two and three months' calls are easily negotiated in the active stocks. Moreover it is curious to note that only in Eng- lish is it easy to express in one term the various positions relating to option dealing. Both the French and the German expressions for any option other than a plain call are as a rule awkward frequently even ambiguous. The difficulty of expressing " which way " a person intends to deal is sometimes overcome in German by adding on at the end of the sentence, OPTION-DEALING ABROAD. 59 " I remain still " (Ich bleibe still), or " you remain still " (Ihr bleibet still), which means in the first case yo2i are giving the option money, and in the latter / am giving the option money. A certain confusion of the English and German option expressions is brought about by the different sense in which the words to give and to take are used in the two languages. In English, to "give for the call" or to "give option money " means to buy the option, whereas in German geben is generally used in the sense of "to sell". Again, nehmen means to take, but the German word conveys the idea of buying when applied to transactions in stocks. The French language provides very few direct and clear expressions in connection with option dealings. An option is known as une option or une prime (a premium), but no good expression exists for either a call or a put, the former being known as une prime, and the latter, on the rare occasions when it may be required, being interpreted as " the right to be able to deliver ". The terms for the call and put in German are more expressive. They are " the forward pre- mium " (Vorpramie) and the " back premium " (Ruck- prdmie). In Germany the put-and-call is treated some- what differently from the London method. It is called Die Stellage for which no English equivalent can be found, but which corresponds with the American ex- pression "straddle". A put-and-call of 2% at 8o covers a range of 4/ from 78 to 82 ; this 4% range or straddle is called the Stellage in German. There- 60 OPTION-DEALING ABROAD. fore the straddle or Stellage is twice the put-and- call and four times the single option. The term call o' more finds an equivalent in German, " the option with more " (Option auf mehr, or Pramie mit nock), but none in French. The best expression that the French language can provide for the call of more is " the right of being able to claim the same quantity," but as this operation is hardly ever practised in France, it does not matter much. The custom of speaking of " so much option money at such and such a price " is only prevalent in England. The foreign mode of expression, "a certain price, of which so much is option money," is convenient in rela- tion to calls, but breaks down completely if one attempts to apply it to puts. Give f call of ^5000 stock at 80 is very neatly turned as " Achetez, 5000 at 8of, dont f ," or " Kaufet, 5000 zu 8of , dont f ". But where are we when we want to telegraph to Paris with as much economy as is consistent with business principles, *' Give f put of 5000 at 80," and have to say, " Payez ^! pour avoir le droit de pouvoir livrer 5000 a 80 "? Again, in a call o' more or put o' more transaction, there is a crispness in the English expression which leaves no doubt as to which way the person giving his instructions wishes to act. It is quite clear that any one who desires to buy call o' more or to sell put o' more is a giver of option money, and that he would be a taker of option money if his instructions read "sell call o' more," or " buy put o' more ". The intention of the operator, however, is not quite so transparent when OPTION-DEALING ABROAD. his instructions are given in such terms as, " Achetez, 2000 a 80, donnant le droit de pouvoir livrer autant" or " Kaufet, 2000 zii 80, mit einmal nock Ruck- pramie ". The following brief vocabulary in English, French and German of expressions incidental to dealing in stocks, more particularly in relation to optional trans- actions, may be of some little use : 62 OPTION-DEALING ABROAD. 2 e - r tr \D v^) **W n ^ * S ' *- *a tl -Is ** s e r 3 oJ don amie a a ., 1 5 -S" 2 2 3 -t-t +j etf JJ ^-" *J 3 ' D "= ,2 ;ri< vH : u 3 t 3 &.-S p- 3 M t: - e dont lchem ^ 'C4 j_, fr'gj *^ ^ "^ 0-1 n-l "V, > ^j g 2 t "9 rt JJ 'o .'5 III ^5-^ '.111^1^11 djTJ-O-O.^^.ti-O a c c rt rt i-3 rtj 331) a.^ 5 o CTJ *j-g. O :j ? U M M - 1 C O t ^i<5 13 5J ^_ P *-* *-^ ^4> s * 4|4|4gj|3 2 3 M -S " ii -5 u ^ S ^-i= x: c o o.Ss *> > .< 0> 3 S 3iJ -O rt u - ^ 3 > < a ^ o'o ' O E 3 J2 " ~" 3 c - u. u rt .> > OJ _E o, u 3 3 73 JS N s this account. La prime echoit cette i next account. La prime echoit la liqi hree months ago. L'option est echue il igh. Le report est cher. n is stiff. . Le deport est cher. s in of the stock. 11 n'y a pas de reporte rs on the stock. Personne ne veut se fi eg w a u - J S g u T3.2; -^ LO OJ t.2 15 CJ t> D "-> x o J3 sra'S.s'-gjl X X u o "0 " v > "So ^ -""Oo C C C c 2-2 g C V W 'l"c g | o G "^ . "S.'o. 5 >>0 g 1 '|.'i^ s s O O O U J2 Erie Shares 2l/ , Milwaukee Shares 5% all on the same rough and ready principle. Now, is it not possible to ascertain by statistics a figure which should represent more accurately the "probable risk" run than one which has been determined, in the first place, by guess work, and in the second, by the speculative impulse of the moment. The writer is of opinion that the risk can be ascertained with a considerable degree of accuracy ; and in this belief he has selected some of the principal speculative stocks and traced their fluctuations from 5 66 THE VALUE OF THE PUT-AND-CALL. week to week over a period of seven years from January, 1888, to December, 1894. The price of each week has been compared with those of the previous week, fortnight, month, two months, and three months (the fluctuations being carried out in columns), and averages have been taken over the whole period in question. The stocks selected for the purpose are : Consols, Brighton 'A,' Spanish 4%, Rio Tinto Shares, De Beers Shares (since 1890, five years), and the fol- lowing shares in the American market : Erie, Norfolk and Western, Union Pacific, Chicago, Milwaukee and St. Paul, and Louisville and Nashville. During the seven years under review these ten representative stocks have been subject to every kind of influence, financial and political ; they have seen times of utter stagnation, and times of the greatest activity ; weak markets and strong markets ; alternate periods of excessive optimism and desperate depression, and during the whole term they have moved up and down consistently with the spirit of the seasons through which they were passing, the fluctuations at one moment being rapid and violent, at another almost imperceptible. If, therefore, an average be ascertained of the fluctuations for given periods in the market prices of these representative stocks, would not that average form a fair basis upon which to calculate the expected performance of those particular stocks in the immediate future ? In fact, does it not come to a question of insurance pure and simple, a premium THE VALUE OF THE PUT-AND-CALL. 6/ being asked to cover a risk ascertained by a kind of actuarial calculation ? Very nearly, although there is a difference between this and other classes of insurance ; were it not so, one could reduce Stock Exchange operations to a certainty, which is known, to borrow Euclid's expression, to be absurd. The difference lies partly in the fact that the statistics governing the premiums exacted for insurances upon life, fire, accident, etc., are obtained with greater accuracy from results spread over a much longer period than it would be possible, or even useful, to do in the case of stocks, and that the conditions from which those results fol- low are much more regular and reliable. Thus, a life insurance company knows that out of one thousand " healthy males " of thirty years of age, it can, with the greatest amount of certainty, expect eight or nine to disappear from the scene of its actuarial calcula- tions before the age of thirty-one. In other words, the " cost of carrying the life " for one year of a man aged thirty, of robust health and good habits, is ascer- tained to be under ^"9 per ^"1000. Whatever the company can charge over and above this amount, plus the working expense, must be its profit, always pro- vided that it can do sufficient business to establish an average. And it is precisely these last words that express the great difference existing between the insurance against fluctuation of stocks and most other classes of insurance. To calculate the value of a risk is one thing, but to make a profit by dealing on that basis is quite another. An individual might insure the life of 68 THE VALUE OF THE PUT-AND-CALL. another to the extent of .1000 for ,30 per annum (on the assumption that the actuarial risk was ^15), and consider that he was making 1 5 a year by the trans- action ; but if the insured dies in the first year there is a loss of .970 in spite of all actuarial reckoning. He must "take the money" very many times to make it pay. It is just so with the taker of option money. Not only must he ascertain the average past behaviour of the stock he is about to deal in, but he must be careful that he can sell this risk a sufficient number of times during the year to establish the average upon which his premium is based. Now, most people who are conversant with the nature of speculative transactions in stocks, and with options in particular, will know that owing to the fickle nature of givers of option money it is impossible to establish the average as suggested above. In actual practice, it is found by option dealers that, unlike other classes of insurers who are willing, e.g., to insure their lives although they are in the best of health and spirits at the moment, or their houses in spite of their enter- taining no immediate fear of being burnt out, the giver of option money only seeks protection when he con- siders that the option money paid does not anywhere nearly represent the risk of which he is relieving him- self by passing it on to his taker. There is not that noble unselfishness about a buyer of a put or a call which is displayed by the man who insures his life only because "all men are mortal," and provision must be made for his little ones. Indeed, where would our THE VALUE OF THE PUT-AND-CALL. 69 great life insurance companies be if they only re- ceived proposals from people who came in because they were not feeling very well? It amounts to this, that the greatest demand for options springs up at a time when it is least profitable for the taker to operate, when dealing against the option in the firm stock is fraught with the most serious danger and diffi- culty ; and, per contra, just when the option taker has a chance of recouping his losses by "running the put- and-call " in a dull and inactive market, he finds that there are " no givers " / Then, it may be asked, how is it possible ever to find a taker of option money at any- thing like a reasonable rate ? The answer is that the option dealer does not work upon any regular system or actuarial basis, but is guided in his operations mainly by the speculative impulse of the moment. This speculative impulse does not exist in any other description of insurance, and had it existed to any appreciable extent, the life of the great insurance cor- porations would be as extinct at the present moment as is the business of the majority of the great option dealers who have found by experience that it is the givers, and not the takers, of option money who have gained the advantage in the long run. A comparison of the table of the Average Fluctuations with lists of option quotations ruling in the market during past years will suffice to illustrate the argument that takers of option money have been carrying on an insurance business with no margin for profit and working ex- penses, even if they could rely on being able to take 7O THE VALUE OF THE PUT-AND-CALL. the same amount of option money on the same quan- tity of stock all the year round and for many years in succession. To lay down a distinct rule for the amount which,, in order to provide a reasonable margin for profit and working expenses, it would be necessary to add in the shape of ''loading" to the option values, as set out at the end of this chapter, would be extremely difficult ; for the conditions of the markets vary so much that what might appear a liberal allowance at one time would be inadequate at another. It is safe to assert, however, that in order to carry an option-taking busi- ness to a successful issue it would be essential : Firstly, to ascertain the past average fluctuations over a considerable period of time of the stock to be operated in. Secondly, to consider whether there is any special influence at work calculated to modify that average result in the immediate future (such as a particular scarcity of the stock for delivery, financial strain, or probability of political complications). Thirdly, to accept risks on approximately the same amounts of stock at regular intervals of time. Fourthly, to add to the " average value " of the put and call an amount which will give a fair margin of profit and allowance for working expenses. Fifthly, to make provision for possible default on the part of the giver (since the option money only becomes payable at the end of the option period), and for special contingencies, such as large differences or THE VALUE OF THE PUT-AND-CALL. 71 bad debts on option stock carried over through buying one half of the stock to convert the call into a put-and- call or loss through an unexpected rise in the money rate, none of these mischances being provided for in the "average value" tables, which have been calculated simply from the average fluctuations. Sixthly and lastly. To be careful that, having once accepted a risk, the option shall be allowed to run to the end of the option period without being tampered with by hedging operations in the firm stock or "cutting the loss" before its time, and that at the expiry of the option the profit or loss shall be taken as final and the position be absolutely closed. Neglect of any of these conditions would com- pletely spoil the average and convert a stocks insurance business into a mere gamble. Let us examine how far they have been observed in the quotations of options for two months and three months respectively in two of the leading speculative shares of the American railroad market Milwaukee shares and Louisville and Nash- ville. Taking the first-named stock we find that in 1888 fifty-two fluctuations of two months averaged 4'47/ ; the same number of fluctuations in 1889 averaged 3 - O2/o; in 1890, 6'O5/ 1 in 1891, 4'63/ ; in 1892, 2'88/ 1 in 1893, 6*48% ; and in 1894, 4'29/ showing a grand average over the seven years of 4*54%- The three months' fluctuations in the same stock come out as follows : In 1888, 4*20% I in 1889, 3* 16% ; in 1890, 8'ii c / c ; in 1891, 6'jo/ ; in 1892, 2*9O/ ; in THE VALUE OF THE PUT-AND-CALL. 1890, 1891, 1892, 5-43% 477% 4'3 2 % 2-88% 5 '4!% 4'53% t'02% 1-05% 1893, 7'02/ ; in 1894, 5 '40% giving a grand average in seven years of 5'29/o- By the same process we find that the two months and three months' fluctuations of Louisville and Nash- ville shares were Two Months. Three Months. 1888, 1889, - - ' C T C/ Average, * 5 o Average, 4'45/ - 4 59 /, 5'34%- 2-90/0 7-28% 1894, - - 4'53%J 5 '40% Now, to put the argument into a practical form we will assume that it would have been possible for an individual or a company to take 4*45% for the put-and- call for two months of 1000 Louisville Shares once every week from ist January, 1888, to 3ist December, 1894 ; that it was not necessary, in order to do this, to take for the call of 2000 shares and buy 1000 shares, thereby indirectly increasing the risk and working expenses ; that no bad debts were incurred by givers failing to pay up at the end of the time ; that every transaction was closed at the expiry of the option, and that no unfortunate hedge against a dangerous-looking option was ever done during its currency. The taker would have had a running risk of 8000 shares against him, one option maturing every week and another taking its place ; he would have dealt fifty-two times in 1000 shares in each year, and again fifty-two times THE VALUE OF THE PUT-AND-CALL. 73 in loco shares in re-buying or re-selling to close his position; that is, in 104,000 shares (of $100 each), or in a total of 728,000 shares in the seven years, equal to a turnover (taking an average price of 60) of ;8, 750,000, with a result of no profit, many heartaches, and the whole of his working expenses to the debit of the account. But suppose that an individual dealer could conduct an option business on the above scale at a working expense of ^1300 per annum, inclusive of bad debts, and that, being a modest individual, he would be will- ing to run a permanent risk against himself of 8000 shares for about .5000 a year profit ; finally, that he uses in his option business only an amount of capital sufficient to cover the loss on 8000 shares in the greatest two months' fluctuation in Louisville known during the last seven years (i6j/ in November, 1890), say ,26,000 ; he would then have to charge for the option (1) The " average value," say - - 4|-/o (2) Proportion of working cost ^1300 -% (3) Proportion of 5% interest on a capital of .26,000 - - -J-% (4) Other contingencies - - ^% (5) Margin of profit - 4% Total - 5f% Thus, by taking every week 5 put-and-call of 1000 Louisville Shares for two months ahead, and closing the operation in each case at option time, a taker 5* 74 THE VALUE OF THE PUT-AND-CALL. would secure a profit in the average of SJ per share, equal to ,5200 on 52,000 shares. On the basis of 5^ his profit would be ^"2600, and at 4-| he would have paid his working expenses and the interest on his capital, but have no profit. Now, to turn for one moment to fact, notice that : In the first week of January, 1895, the two months single options in Louisville and Nashville Shares, and o * Chicago Milwaukee and St. Paul Shares were quoted 8 1 J, equal to %Z\for the put-and- call ! The three months' single options of these two stocks on the same date were quoted respectively $2^ and *32f, equal to 84^ put-and-call on Louisville and 64} on Milwaukee. The " average values " for three months come out 5 '34% on Louisville and 5*29% on Milwaukee, and, treating these figures in the same manner as we have done in the case of the two months options, we find that, on the basis of 86J, the option taker would have averaged a profit of SJ per share during the seven years, 1888-1894, and that at the premium of $5f he would just have paid his expenses and interest on capital. At any lower premium he would have worked at a loss. It is not the intention of the writer to illustrate any- further the difference between the actual market prices of options and their "average values". The fore- going examples have been quoted with a view to suggesting further investigation on the part of the reader, and for the purpose of placing before him a method of examination which may make the study of THE VALUE OF THE PUT-AND-CALL. 75 options and option dealing something better than dry business and dull figures. The appended table of average values is by no means complete, although it has been prepared, as far as it goes, with a consider- able amount of care, and the main object of intro- ducing it into this little volume is to offer a practical reply to those who have been heard to say : "If the option dealer thinks it good enough to take the money, it cannot be ' business ' for me to give it ". TABLE OF AVERAGE VALUES. The approximate value of the "put and call" of some leading stocks, as ascertained by the average fluctuations for the periods in question, between ist January, 1888, and 3ist December, 1894. . a .c t 1 i m 8, gg I ll ! Is > ll i ll P 1888 '25 40 '67 98 1-18 1889 19 29 '39 58 79 1890 30 '49 72 I -06 i'34 CONSOLS. 1891 25 36 '47 64 75 1892 1893 '24 23 '9 79 '85 I'lO 1-07 18* '22 24 38 37 70 57 1-17 86 I 12 1888 gi i '39 2'01 3'69 5'65 1889 2'2I 3-80 6-08 7'3 l 1898 1-26 2-09 2'97 3-46 4-00 BRIGHTON "A". 1892 Si r88 1-60 2-99 271 4'6 4 475 6-40 1893 1894 1-23 ri6 1.18 2-00 1-69 1-83 3-04 2-87 2-90 4'65 3'92 4'45 6-25 473 5-66 1888 46 74 1-14 1-97 2-88 1889 50 78 1-29 178 1-99 1890 '52 80 1-20 i'74 2-05 SPANISH. 1891 75 i -08 I'6 3 2-25 2-63 1892 I '22 2-85 3-19 1893 61 I'OO 1*63 2'13 2-24 1894 '59 60 8 7 92 1-30 1-44 2-31 2-14 3-19 2'59 1888 62 88 I-I4 2-14 2'95 1889 61 96 1-69 3-02 3'93 1890 '5 80 i'55 2-05 2-64 RIO TINTO. '891 '42 60 81 1-09 1-29 1892 '33 '5 1 86 I '09 1893 '22 '37 '57 83 i -06 1894 28 42 38 64 60 1-03 91 i '59 I'02 1-98 DE BEERS IsSg 44 '59 92 I V 27 1-40 1891 '35 50 74 1-25 (five years only). ,892 '22 '37 58 I -06 i '47 1893 '32 '47 77 I '22 r6i 1894 32 '33 '39 46 66 '73 1-07 IMS 1-26 i '39 1888 1889 72 62 '97 70 1-64 '97 3 2-51 i '43 1890 '57 '97 2-36 2-88 ERIES. 1891 '93 1-24 1-97 3'io 3-85 1892 90 1*25 1-63 2-07 2'22 1893 90 1-32 1-89 273 3-22 1894 56 '74 '83 1-04 i '43 1-58 2-06 2 '33 2'37 2-64 1888 i '45 2'09 3-13 4'47 4'20 l889 1-27 2-44 3'02 3'i6 l8OO 1-16 2'2I 3'45 6-04 8-n MILWAUKEE. l89I 1-28 1-81 274 4-63 670 1892 1-19 i '44 2'00 2-88 2-90 1893 i '95 2-94 4'22 6-48 7-02 1894 1-18 '3S 2'OI 2'00 2'97 2-99 4-29 4'54 4-97 5-29 1888 no i'55 2-60 3'8 4 4-19 1889 I'22 176 3'5 5'43 8-02 LOUISVILLE. 1890 1891 I'25 I'49 2-04 2-05 3-20 477 4'32 5'05 4'59 1892 I-ig i '44 2'OO 2-88 2-90 1893 175 279 3-29 5'4 Z 7'28 1894 '94 1-27 1-67 1-90 3'3 2-90 4'53 4 '45 5'40 S'34 1888 92 i'33 2-31 3-19 3'6o 1889 78 I'22 1-96 3 - 01 3'63 NORFOLK PREF. 1890 84 I'OO I '45 1-32 2-19 2-25 3'i6 3-03 3-21 2-90 1892 75 I'22 1-67 2'39 2'59 1893 '97 i'53 2-04 3'47 470 1894 87 '87 1-36 '*34 2-07 278 3*00 3-10 3 '39 1888 ri8 1-63 2-13 2-87 3'48 1889 1-07 1-42 1-99 2-93 3'29 UNION PACIFIC. 1890 1891 i '39 1-97 2'OO 3'oi 2-62 473 3'25 6-17 3'30 1892 I'3I 1-89 3'02 3'82 1893 t'38 2'II 3-09 4'37 4'92 1894 79 M3 i'34 1-68 2-40 2-94 3-44 3-23 4-03 HIGGINS'S . . PATENT . . CALCULATING TRIANGLE s ing? patent Calculating Triangli (AMERICAN PARITIES). Fig 1. Fig 2. HIS Instrument calculates instantaneously the English equivalents of New York prices at any rate of exchange between $4.80 and $4.90. Figure i shows the two Scales fixed at the rate 4.90. Parities at any lower exchange can be read off by moving the indicator and cursor as shown in Figure 2. The machine can also be applied to the calculation of English parities of Dutch prices for American securities, by multiplying the Dutch exchange by 4 and using the American rates of exchange. Thus the London parity of 65 Amsterdam at the exchange of fl. 12.10 is the same as the London parity of the American price 65 at the exchange of 4.84. PRICE In Brass and Mahogany with Case -330 Measuring 22 in. x 8 in. ** J^xtracts from J^ress AJotices. "THE TIMES." We have been shown an ingenious "Calculating Triangle" which is designed to work out on a geometrical principle the English parities of New York prices at any rate of exchange from $4.80 to $4.90. The idea (of making calculations by mechanical means) is not new, but Mr. Leonard R. Higgins claims that his machine is easier and more expeditious to work with than any other. "THE FINANCIAL NEWS." Mr. Leonard R. Higgins, of the Stock Exchange, has invented an ingenious time and labour saving instrument which he calls a " Calculating Triangle." It works out on a geometrical principle the English parities of New York prices at any rate of exchange between $4.80 and $4.90 ..... The operation is very simple and accurate, the foreign price, its English equivalent and the rate of exchange being always easily read off, at whatever figures the instrument is set ..... These instruments will come as a boon and a blessing to bankers, brokers and others to whom time and accuracy are equally important. "THE FINANCIAL TIMES." The calculating instrument invented and patented by Mr. Leonard R. Higgins deserves some notice on account of the novelty of the principle on .on which it is based. The machine in question indicates in a single operation, with perfect accuracy, the English parities of New York prices at any rate of exchange ..... The calculation of proportions on a geometrical principle (without the use of logarithmic scales generally used in mechanical calculations) strikes us as being a novel invention, showing considerable ingenuity on the part of the originator. "THE BULLIONIST." Very ingenious is Mr. Leonard R. Higgins's invention which he calls his " Calculating Triangle. " .... The Triangle is worked in an extremely simple manner ..... Whether Mr. Higgins's highly ingenious inven- tion will ever become a monetary success remains to be seen. "THE STAR." We have had an opportunity of inspecting a most ingenious instrument patented by Mr. Leonard R. Higgins, of the London Stock Exchange, described as a "Calculating Triangle." .... What especially impresses us in the instrument is that Mr. Higgins had it brought to his mind in thinking over the second proposition of the sixth book of Euclid. This ought to put up the price of "Todhunters" which hitherto have been useful mainly in getting fellows plucked for examinations. "THE MONEY MARKET REVIEW" An instrument invented by Mr. Leonard R. Higgins, which should prove a useful addition to the furniture of bankers' and brokers' offices, .... connects with the greatest accuracy the prices of one country into the parities of another at any rate of exchange ..... unlike any other mechanical calculator we have seen. "THE SCOTTISH LEADER." A clever invention of Mr. Leonard R. Higgins for automatically calculating English equivalents of New York prices ..... The strictest accuracy is insured and the instrument is simplicity itself. W. F. STANLEY (Maker,) 4, Great Turnstile, Holborn, W.C. CATALOGUE COMMERCIAL AND OTHER WORKS PUBLISHED AND SOLD BY EFFINGKHAM WILSON, ^ublis^r, printer, gookstlltr, gmber, ^ngrsfar, anb Siaiiotwr, 11, ROYAL EXCHANGE, LONDON. TO WHICH IS ADDED A LIST OF TELEGRAPH CODES, VALUABLE BOOKS of REFERENCE essential to COMMERCIAL ESTABLISH- MENTS and PUBLIC COMPANIES. In addition to the Works enumerated in this Catalogue, THE BOOKS OF ALL OTHEK PUBLISHERS may be had at this Establishment immediately on their Publication. EFFINGHAM WILSON undertakes the printing and publishing of Pamphlets and Books of every description upon Commission. Estimates given, and Conditions of Publication may be had on application. June, 1896. LONDON: EFFINGHAM WILSON, ROYAL EXCHANGE. INDEX. Arbitrages et Parites PAGE Haupt, O 13 Willdey's American Stocks 19 Arbitration London Chamber of 17 Lynch, H. Foulks 15 Auditors Pixley 24 Banking Banking. History of 4 Banking Law (Wallace and M'Neil) 24 Banks, Bankers, and Banking 16 English and Foreign (Attfield) 9 Gilbart's History and Principles .. 22 Hankey (Thomson) 13 Hutchison, J 13 Journal Institute of Bankers 14 London Banks and Kindred Com- panies 23 Macleod's Banking 23 Moxon's English Practical Banking 23 Questions on Banking Practice.... 16 Eae's Country Banker 24 Smith's Banker and Customer .... 17 Bankruptcy McEwen (Accounts) 15 Stewart (Law of) 7 Bills of Exchange Byles 21 Chalmers 22 Kolkenbeck (Stamp Duties on) 14 Smith 7 Bimetallism- List ofWorks 20 Bookkeeping Cariss 9 Carr (Investors) 8 Carter 22 Hamilton and Ball 22 Harlow's Examination Questions.. 13 Holah 8 Jackson 14 Richardson (Weekly Newspapers) . . 16 Sawyer 17 Seebohm's (Theory) 8 Van de Linde 18 "Warner (Stock Exchange) 19 Clerks- Commercial Handbook 8 Companion to " Solicitor's Clerk " . . 14 Counting-house Guide 17 Kennedy (Stockbrokers) 7 Merchant's 8 School to Office 8 Solicitor's 14 Correspondence (Commercial) - Anderson 21 Beaure 9 Martin (Stockbrokers) 7 McGoun 23 I Counting House PAGE Bithell (Dictionary) 21 Crowley 8 Pearce'. 8 Tate 18 County Court Jones 14 Currency and Finance Aldenham (Lord) 9 Baeehot 21 Barclay (Kobert) 9 Clare's Money Market Primer 10 Cobb 10 Cuthbertson 10 Del Mar's History 10 Del Mar's Science of Money 11 Ellis 11 Haupt 13 Jevons 22 Dictionaries Counting House (Bithell) 20 Directories Brewery (Duncan) 11 Directory of Directors * 24 Mining Manual (Skinner) 24 Directors Haycraft (Liabilities and Duties) . . 8 Palmer 23 Exchanges- Clare 10 Goschen 13 Jevons 22 Tate's Modern Cambist 18 Exchange Tables Bartlett-Amati (various) 21 Dollar (Eastern) 14 Garratt (South American) 12 Lecoffre (French) 14 Merces (Indian) 16 Schultz (American) 17 Schultz (German) .' 17 Insurance, Fire and Marine Lowndes 22 McArthur 23 Owen 23 Interest Tables Bosanquet 9 Crosbie and Law (Product) 10 Cummins (2r/ ) 10 Gilbert 22 Gumersall 13 Indian Interest (Merces) 16 Laurie 23 Lecoffre's Universal 14 Laurie (Simple and High Eate) . . 23 Lewis (Time Tables) 15 Ranee (Compound) 24 Rutter 17 Wilhelm (Compound) 19 LONDON: EFFINGHAM WILSON, ROYAL EXCHANGE. PAGE Investors (see also Stock Exchange Manuals) Art of Investing 21 Bookkeeping (Carr) 8 Duncan on Investment and Specu- lation 11 Investment Profit Tables 18 Houses and Land 8 How to Invest Money 8 Ledger . 19 'Review' 22 Joint-Stock Companies Alpe's Stamp Duties 21 Buckley 21 Cummins' Formation of Accounts . 10 Fitzpatrick (Secretary) 22 Fowke'sCompanies Acts,1862to 1890 22 Haycraft (Directors) 8 Jordan 22 Palgrave (Chairman) 23 Palmer (Precedents) 23 Smith 7 Watts (Promoters) 24 Legal and Useful Handy Books- List of 7, 8 Mining- Anderson (Prospectors) 24 Beeman's Australian MiningManual 9 Gabbott's How to Invest in Mines 12 Goldmann (South African Mining) 12, 13 Kindell'B African Market Manual. . 14 Skinner (Mining Manual) 24 Western Australia Investor's Guide 13 Miscellaneous Author's Guide 19 Copyright Law 10 Cotton Trade of Great Britain .... 11 District and Parish Councils (Lithi- by) 15 Egyptian State Debt 22 Fire Surveys (Sir Eyre M. Shaw).. 17 Gresharn, Sir Thomas (Life of) 9 Ham's Customs Year Book 13 Ham's Inland Revenue Year Book. . 13 Imperial Customs Union 4 Legal Forms for Common Use 17 Patent Law and Practice (Emery) 1 1 Public Meetings 18 Red Palmer 18 Urquhart's Port Charges 24 Money Market (see Currency and Finance). Pamphlets 19 Prices Dunsford (Railways) 11 Ellis..... 11 Mathieson (Stocks) 15 Railways American as Investments 18 American and British Investors. . . . 18 Bradshaw (Shareholders) 21 Railways continued PAGE Dunsford (Dividends and Prices) . . 11 Home Rails as Investments 18 Mathieson's Traffics 15 Poor's Manual (American) 16 Railroad Report (Anatomy of a) . . 19 Railways in India 12 Ready Reckoners (see also Exchange Tables, Interest,. &c.) Blewert (Stock) 21 Buyers' and Sellers' (Ferguson) . . 8 Goodfellow (Shipmasters) 22 Ingram (Yards) 14 Louis, Anglo-French 23 Merces (Indian) 16 Robinson (Share) 17 Silver Tables (Bar Silver) 12 Sinking Fund and Annuity Tables- Ranee 24 Willich 24 Speculation (see Investors and Stock Exchange) . Stock Exchange Manuals, &c. Blewert (Stock Tables) 21 Brewery Manual (Duncan) 11 Burdctt's Official Intelligence .... 9 Contango Tables 12 Fenn on the Funds, English and Foreign 12 Laws and Customs (Melsheirner) . . 16 Laws, English and Foreign Funds (Royle) 17 Mining Manual (Skinner) 24 Options (Castelli) 10 Poor's American Railroad Manual.. 16 Put-and-Call 4 Railways (Bradshaw's Manual) 21 Rapid Share Calculator 11 Redeemable Stocks (a Diagram) .. 9 Registration of Transfers 11 Robinson (Share Tables) 17 Rules and Usages (Stutfield) 18 Statesman's Year Book 24 Stock Exchange Values, 1885-1895 19 Stock Exchange Year Book 24 Willdey's American Stocks 19 Tables (see Exchange Tables, Interest Tables, Ready Reckoners, and Sinking Fund and Annuity Tables, &c.). Telegraph Codes Ager's (list of) 5 Lieber's Standard 4 Miscellaneous (list of) 6 Trustees- Investment of Trust Funds 7 Trustees, their Duties, &c 7 Marrack's Statutory Trust Invest- ments 15 Wilson's Legal and Useful Handy Books List 7,8 LONDON : EFFINGHAM WILSON, ROYAL EXCHANGE. JUST OVER FROM AMERICA. Price Two Guineas net. LIEBER'S STANDARD TELEGRAPHIC CODE, By B. FKANKIN LIEBER. The code is of 800 pages, and contains over 75,000 code-words, 25,000 con- sisting of tables. There are 10,000 extra ciphers, giving ample opportunity for special phrases. The code words employed are from the " Official Vocabu- lary." The compilers having only used ciphers from "A " to " F," au oppor- tunity is left to cablers to construct a large private and separate code for their own particular and individual use. The arrangement of the sentences is strictly alphabetical. For Bankers, Brokers, Manufacturers, Merchants, Stockbroker's, and the Legal Profession. LIBBER'S MANUAL Published bimon thly, Subscription 12s. 6d. per Annum. The names of holders of the Code are inserted free of charge in the above Manual, and care should be taken that, the name is sent for insertion at once on purchase. A subscription to this Manual cannot be too strongly advised. A HISTORY OF THE BANKING OF ALL NATIONS In Four Royal 8vo volumes, Price 5 complete. VOLS. I AND II Now READY. Vol. I contains the History of Banking in the United States. By WILLIAM G. SlTMNEH. VOL. II contains History of Banking in Great Britain. By HENET DUNNING MACLEOD. History of Bunking in Russia. By ANT. E. HOBN. History of Savings Banks in the United States. By JOHN P. TOWNSEND. VOLS III and IV (in preparation) will contain History of Banking in the Latin Nations, Germany and Austria-Hungary, Scandinavian Nations, Holland, Canada, China, Japan, &c. THE PUT-AND-CALL. By L. HIGGINS. Price 3*. Qd. net. IMPERIAL CUSTOMS UNION. By K. N. MACFEE, M.A. Price 2s. 6d. 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